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02.04 Uncertainty and Variability in Vibro-Acoustics

Comparison of quadrature and regression based generalized polynomial chaos expansions for structural acoustics
Time: 1:00 pm

Author: Gage Walters

Abstract ID: 1670

This work performs a direct comparison between generalized polynomial chaos (GPC) expansion techniques applied to structural acoustic problems. Broadly, the GPC techniques are grouped in two categories: , where the stochastic sampling is predetermined according to a quadrature rule; and , where an arbitrary selection of points is used as long as they are a representative sample of the random input. As a baseline comparison, Monte Carlo type simulations are also performed although they take many more sampling points. The test problems considered include both canonical and more applied cases that exemplify the features and types of calculations commonly arising in vibrations and acoustics. A range of different numbers of random input variables are considered. The primary point of comparison between the methods is the number of sampling points they require to generate an accurate GPC expansion. This is due to the general consideration that the most expensive part of a GPC analysis is evaluating the deterministic problem of interest; thus the method with the fewest sampling points will often be the fastest. Accuracy of each GPC expansion is judged using several metrics including basic statistical moments as well as features of the actual reconstructed probability density function.

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Predicting robust complete and full band gaps in three-dimensional frame structures
Time: 3:40 pm

Author: Luiz Henrique Marra da Silva Ribeiro

Abstract ID: 1842

Vibration can cause structural damage in dynamic systems when not designed properly. Recently, several approaches are emerging in structural dynamics as possible alternatives for passive vibration and noise control, such as phononic crystals and metamaterials. In this work, a three-dimensional frame that presents intersection of longitudinal, flexural and torsional band gaps is investigated. For periodic structures, the Irreducible Brillion Zone (IBZ) gives information for any possible angle of propagation of a wave. The manufacturing process induces variability along each three-dimensional frame element. The present study verifies the robustness of the band gaps of the three-dimensional structure against spatially varying geometry and mechanical properties. The spatial random fields are modeled using the expansion optimal linear estimator (EOLE). Bayesian statistics is used to infer on the stochastic response simulated using the Monte Carlo method combined with the EOLE. The three-dimensional frame is modeled via Euler-Bernoulli beam and ordinary shaft theories as well as  with Timoshenko and Saint-Venant theories. It is shown that the three-dimensional frame structure exhibits a complete (for all waves) and full (throughout the IBZ) robust band gap against the proposed variability. Both models are able to predict this robust band gap.

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Assessment of digital image correlation vibrometry in the presence of thermal flow disturbance
Time: 1:40 pm

Author: Kenji Homma

Abstract ID: 2543

Digital Image Correlation (DIC) is an image-based method for measuring displacement and/or stain on the surface of a structure.  When coupled with a stereo pair of highspeed cameras, DIC can also capture three-dimensional dynamic deformation of a structure under vibratory loading.  However, high frequency and small amplitude displacement typically associated with structural vibrations mean that extra care is required during measurement and data processing. It becomes more challenging when thermal disturbances are present in the optical path, for example from a heated air flow, which introduces extraneous noise due to disturbances in the refractive index.  In the present study, a simple composite plate was vibrated under a shaker excitation and stereo DIC measurements were performed. The obtained vibratory displacement results were compared against accelerometers and a laser Doppler vibrometer.  Heated air flow was introduced in front of the plate to observe the effects of thermal disturbances on the DIC measurements.  Although the contributions from the thermal disturbances were clearly visible in the DIC displacement data, it was shown that the vibratory deflections of the structure could still be extracted by post processing of the DIC data.

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Welding distortion generated uncertainties in the vibrational behavior of a ladder-like structure
Time: 12:40 pm

Author: David Sipos

Abstract ID: 2844

Recent developments in acoustic simulation methods allowed engineers to assess the vibroacoustic behavior of various type of structures within a virtual environment, thus allowing the replacement of prototype-based development with simulations. However, there are some factors, that cannot be considered in simulations in advance. In the present study, the effect of the distortions generated due to welding on a ladder-like structure equipped with flat plates was investigated. The measured acceleration frequency response functions were compared to finite element simulation results. The measured responses differed significantly from the simulation, even in the low frequency range, where the global modes were not expected to be altered or vanished. Investigation of the simulated results revealed that the additional modes were related to the vibration of the plates, which were assumed to be flat, instead of considering the warping caused by the welding process. After measuring the approximate deformation of the plates, an updated simulation model was made, introducing an approximate curvature in them. The results obtained with the updated simulation model performed much better in the low frequency range as well as in the third octave-averaged frequency bands up 1200 Hz. The sensitivity of the warping was also systematically evaluated.

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Variance Quantification of Different Additive Manufacturing Processes for Acoustic Meta Materials
Time: 1:20 pm

Author: Manuel Bopp

Abstract ID: 2211

Many concepts for acoustic meta materials rely on additive manufacturing techniques. Depending on the production process and material of choice, different levels of precision and repeatability can be achieved. In addition, different materials have different mechanical properties, many of which are frequency dependent and cannot easily be measured directly. In this contribution the authors have designed different resonator elements, which have been manufactured utilizing Fused Filament Fabrication with ABSplus and PLA, as well as PolyJet Fabrication with VeroWhitePlus. All structures are computed in FEA to obtain the calculated Eigenfrequencies and mode shapes, with the respective literature values for each material. Furthermore, the dynamic behavior of multiple instances of each structure is measured utilizing a 3D-Laser-Scanning Vibrometer under shaker excitation, to obtain the actual Eigenfrequencies and mode shapes. The results are then analyzed in regards to variance between different print instances, and in regards to accordance between measured and calculated results. Based on previous work and this analysis the parameters of the FEA models are updated to improve the result quality.

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